Process optimization in gas phase dry etching

ABSTRACT

A method of designing a reactor 10. The present reactor design method includes steps of providing a first plasma etching apparatus 10 having a substrate 21 therein. The substrate includes a top surface and a film overlying the top surface, and the film having a top film surface. The present reactor design method also includes chemical etching the top film surface to define a profile 27 on the film, and defining etch rate data from the profile region. A step of extracting a reaction rate constant from the etch rate data, and a step of using the reaction rate constant in designing a second plasma etching apparatus is also included.

This is a Continuation of application Ser. No. 08/433,623 filed May 3,1995, now U.S. Pat. No. 5,711,849, the disclosure of which isincorporated by reference.

BACKGROUND OF THE INVENTION

The present invention relates to integrated circuits and theirmanufacture. The present invention is illustrated in an example withregard to plasma etching, and more particularly to plasma etching ofresist strippers in semiconductor processing. But it will be recognizedthat the invention has a wider range of applicability in othertechnologies such as flat panel displays, large area substrateprocessing, and the like. Merely by way of example, the invention may beapplied in plasma etching of materials such as silicon, silicon dioxide,silicon nitride, polysilicon, photoresist, polyimide, tungsten, amongothers.

Industry utilizes or has proposed several techniques for plasma etching.One such method is conventional chemical gas phase dry etching.Conventional chemical gas phase dry etching relies upon a reactionbetween a neutral gas phase species and a surface material layer,typically for removal. The reaction generally forms volatile productswith the surface material layer for its removal. In such method, theneutral gas phase species may be formed by way of a plasma discharge.

A limitation with the conventional plasma etching technique is obtainingand maintaining etching uniformity within selected predetermined limits.In fact, the conventional technique for obtaining and maintaininguniform etching relies upon a "trial and error" process. The trial anderror process often cannot anticipate the effects of parameter changesfor actual wafer production. Accordingly, the conventional technique forobtaining and maintaining etching uniformity is often costly, laborious,and difficult to achieve.

Another limitation with the conventional plasma etching technique isreaction rates between the etching species and the etched material areoften not available. Accordingly, it is often impossible to anticipateactual etch rates from reaction rate constants since no accuratereaction rate constants are available. In fact, conventional techniquesrequire the actual construction and operation of an etching apparatus toobtain accurate etch rates. Full scale prototype equipment and the useof actual semiconductor wafers are often required, thereby being anexpensive and time consuming process.

From the above it is seen that a method and apparatus of etchingsemiconductor wafers that is easy, reliable, faster, predictable, andcost effective is often desired.

SUMMARY OF THE INVENTION

According to the present invention, a plasma etching method thatincludes determining a reaction rate coefficient based upon etch profiledata is provided. The present plasma etching method provides for an easyand cost effective way to select appropriate etching parameters such asreactor dimensions, temperature, pressure, radio frequency (rf) power,flow rate and the like by way of the etch profile data.

In a specific embodiment, the present invention provides an integratedcircuit fabrication method. The present method includes steps ofproviding a plasma etching apparatus having a substrate therein. Thesubstrate includes a top surface and a film overlying the top surface.The film includes a top film surface. The present method also includeschemically etching the top film surface to define an etching profile onthe film, and defining etch rate data which includes an etch rate and aspatial coordinate from the etching profile. A step of extracting areaction rate constant from the etch rate data, and using the reactionrate constant in adjusting a plasma etching apparatus is also included.

In an alternative specific embodiment, the present invention alsoprovides a method of designing a reactor. The present method includesproviding a first plasma etching apparatus having a substrate therein.The substrate has a top surface and a film overlying the top surface.The film has a top film surface. The present method also includeschemically etching the top film surface to define an etching profile onthe film, and defining etch rate data which has an etch rate and aspatial coordinate from the etching profile. A step of extracting areaction rate constant from the etch rate data, and using the reactionrate constant in designing a second plasma etching apparatus is alsoincluded.

A further alternative embodiment provides another method of fabricatingan integrated circuit device. The present method includes steps ofproviding a uniformity value for an etching reaction. The etchingreaction includes a substrate and etchant species. The present methodalso includes defining etching parameter ranges providing the uniformityvalue. A step of adjusting at least one of the etching parameters toproduce a selected etching rate is also included. The etching rateprovides an etching condition for fabrication of an integrated circuitdevice.

The present invention achieves these benefits in the context of knownprocess technology. However, a further understanding of the nature andadvantages of the present invention may be realized by reference to thelatter portions of the specification and attached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a simplified diagram of a plasma etching apparatus accordingto the present invention;

FIG. 1A is a simplified cross-sectional view of a wafer profileaccording to the plasma etching apparatus of FIG. 1;

FIG. 2 is a simplified diagram of an alternative embodiment of a plasmaetching apparatus according to the present invention;

FIGS. 3-5 are simplified flow diagrams of plasma etching methodsaccording to the present invention;

FIG. 5A is a plot of uniformity, temperature, pressure, and gap for anetching process according to the present invention;

FIG. 6 is a simplified plot of 1 (Ash Rate) vs. LCD plate numberaccording to the present invention;

FIGS. 7-9 illustrate an example with regard to circular substratesaccording to the present invention; and

FIGS. 10-12 illustrate an example with regard to rectangular substratesaccording to the present invention.

DESCRIPTION OF THE SPECIFIC EMBODIMENT

Plasma Etching Apparatus

FIG. 1 is a simplified diagram of a plasma etching apparatus 10according to the present invention. The plasma etching apparatus alsoknown as a co-axial reactor includes at least three processing zones.The three processing zones are defined as a plasma generating zone (PG)13, a transport zone (TZ) 15, a plate stack zone (PS) 17, and others.Also shown are a chemical feed F and exhaust E. The plasma generatingzone provides for reactant species in plasma form and others. Excitationis often derived from a 13.56 MHz rf discharge 8 and may use eithercapacitor plates or a wrapped coil, but can also be derived from othersources. The co-axial reactor 10 also includes a chemical controller 14and a temperature and pressure control 12, among other features.

Chemical effects are often enhanced over ion induced effects and othereffects by way of perforated metal shields 18 to confine the dischargeto a region between an outer wall 16 and shields 18. The co-axialreactor relies substantially upon diffusion to obtain the desiredetching uniformity. The co-axial reactor also relies upon a chemicaletch rate which is diffusion limited. In particular, the chemical etchrate is generally defined as a chemical reaction rate of etchant speciesplus at least a diffusion rate of etchant species. When the diffusionrate of etchant species is much greater than the chemical reaction rate,the chemical etch rate is often determined by the diffusion rate. A moredetailed analysis of such chemical etch rate will be described by way ofthe subsequent embodiments.

Etchant species from the plasma generating zone diffuse through thetransport zone 15 of the reaction chamber, and enter the plate stackzone space over surfaces of substrates 21. A concentration of etchant inthe transport zone, which is often annular, between the plasmagenerating zone and the plate stack zone is defined as n_(o0). Asetchant diffuses radially from the transport zone into the plate stackzone and over surfaces of the substrates, it is consumed by an etchingreaction. A reactant concentration above the substrate can be defined asn_(o) (r,z), where r is the distance from the center of the substrateand z is the distance above the substrate. A diffusive velocity v_(o) ofetchant species in the plate stack zone is characterized by Fick's law.##EQU1##

In a specific embodiment, a gap d_(gap) above the substrate is much lessthan the lateral extent d_(gap) <<r and gas phase mass transferresistance across the small axial distance is negligible so that theaxial (z-direction) term of the concentration gradient can be ignored.The embodiment can be applied without this restriction; however,numerical mesh computer solutions are then required to evaluate thereaction rate constant and uniformity. In the embodiment, the surfaceetching reaction bears a first order form:

    O+S→SO

where

S is a substrate atom (e.g., resist unit "mer"); and

O is the gas-phase etchant (for example oxygen atoms) with certainetching kinetics. The first order etching reaction rate can be definedas follows: ##EQU2## where R_(o) defines a reaction rate;

n_(o) defines a concentration;

A defines a pre-exponential constant;

T defines a temperature;

E_(ACT) defines an activation energy; and

R defines a gas constant.

An example of the first reaction is described in D. L. Flamm and D. M.Manos "Plasma Etching," (1989), which is hereby incorporated byreference for all purposes. Of course, other order reactions, reactionrelations, and models may be applied depending upon the particularapplication.

An example of an etched substrate 21 from the plate stack zone isillustrated by FIG. 1A. The substrate 21 is defined in spatialcoordinates such as z and r. The substrate includes a bottom surface 23,sides 25, and a top surface film 27. As can be seen, the top surfacefilm includes a convex region, or etching profile. The etching profileoccurs by way of different etch rates along the r-direction of thesubstrate corresponding to different etchant species concentrations. Aconcentration profile n_(o) (r,z) is also shown where the greatestconcentration of reactant species exists at the outer periphery of thetop surface film. In the present invention, an etch rate constant may beobtained by correlation to the etching profile. By way of the etch rateconstant, other etching parameters such as certain reactor dimensionsincluding a distance between substrates, pressure, temperature, and thelike are easily calculated.

FIG. 2 illustrates an alternative example of an etching apparatus 50according to the present invention. The etching apparatus 50 is a singlewafer etching apparatus with elements such as a chamber 53, a topelectrode 55, a bottom electrode 57, a power source 59, a platen 64, andothers. The bottom electrode 57 is at a ground potential, and the topelectrode is operably coupled to the power source 59 at a high voltagepotential. A plasma exists in a region 54 between the top electrode 55and the bottom electrode 57, which is often a grid configuration or thelike. Reactant species are directed via power source from a plasmasource to a wafer substrate 61 by diffusion. A temperature and pressurecontroller 67 and a flow controller 69 are also shown. The etchingapparatus also includes a chemical source feed F and an exhaust E. Ofcourse, other elements may also be available based upon the particularapplication.

By way of a plate 63 interposed between the wafer substrate 61 and thebottom electrode 57, the reactant species do not directly bombard thewafer substrate. The plate is preferably made of an inert materialappropriate for the particular etching such as pyrex or glass for resistashing, alumina for fluorine atom etching of silicon, silicon nitride,or silicon dioxide, and the like. In an ashing reaction, the plate isplaced at a distance ranging from about 5 mm to 50 mm and less from thewafer substrate 61. Of course, other dimensions may be used dependingupon the particular application. The reactant species are transportedvia diffusion from the plasma source to the wafer substrate around theperiphery of the plate 63. Accordingly, the reaction rate at the wafersubstrate is controlled by a balance between chemical reaction anddiffusion effects, rather than directional bombardment.

By way of the diffusion effects, an etching rate constant may beobtained for the etching apparatus 50 of FIG. 2. In particular, theetching rate constant derives from a etching profile 65, which can bemeasured by conventional techniques. The present invention uses theetching rate constant to select other etching rate parameters such asreactor dimensions, spacing between the substrate and its adjacentsurface, temperatures, pressures, and the like. But the presentinvention can be used with other reactor types where etching may not becontrolled by diffusion. For example, the present invention provides areaction rate which can be used in the design of reactors wherediffusion does not control such as a directional etcher and the like.The reaction rate constant may also be used in the directional etcher topredict an extent of, for example, undercutting of unprotected sidewallswhile ion bombardment drives reaction in a vertical direction. Ofcourse, the invention may be applied to other reactors such as largebatch, high pressure, chemical, single wafer, and others. The inventioncan also be applied to different substrate materials, and the like.

Plasma Etching Method

FIGS. 3-5 illustrate simplified flow diagrams of plasma etching methodsaccording to the present invention. The present methods provide forimproved etching conditions by wax of a reaction rate constant derivedfrom, for example, an etching profile. It should be noted that thepresent methods as illustrated should not be construed as limiting theinvention as defined in the claims. One of ordinary skill in the artwould easily recognize other applications of the inventions describedhere.

In a specific embodiment, a method 100 of extracting a rate constant fora plasma etching step according to the present invention is illustratedby the flow diagram of FIG. 3. A substrate with an overlying film isplaced into a plasma etching apparatus or the like. The overlying filmis defined as an etching film. In the present embodiment, the overlyingfilm is a photoresist film, but can also be other films such as asilicon film, a polysilicon film, silicon nitride, silicon oxide,polyimide, and the like.

A step of plasma etching the film is performed by step 101. The plasmaetching step occurs at constant pressure and preferably constant plasmasource characteristics. More preferably, the plasma etching step occursisothermally at temperature T₁, but can also be performed with changingtemperatures where temperature and time histories can be monitored.Plasma etching of the film stops before the endpoint (or etch stop).Alternatively, plasma etching stops at a first sign of the endpoint (oretch stop). The plasma etching step preferably stops before etching intoan etch stop layer underlying the film to define a "clean" etchingprofile.

The substrate including etched film is removed from the chamber of theplasma etching apparatus. The etched film includes an etching profile(step 103) made by way of plasma etching (step 101). The etching profileconverts into a relative etch rate, relative concentration ratio, arelative etch depth, and the like at selected spatial coordinates. Therelative etch rate is defined as an etch rate at a selected spatialcoordinate over an etch rate at the substrate edge. The relativeconcentration ratio is defined as a concentration of etchant species ata selected spatial coordinate over a concentration of etchant at thesubstrate edge.

In x-y-z coordinates, the relative etch rate is in the z-direction, andthe spatial coordinates are defined in the x-y coordinates. The etchingprofile is thereby characterized as a relative etch rate u, ax-location, and a y-location u(x,y). In cylindrical coordinates, therelative etch rate is also in the z-direction, and the spatialcoordinates are defined in the r and θ coordinates. The etching profileis characterized as a relative etch rate u, an r-location, and aθ-location u(r, o). An array of data points in either the x-ycoordinates or r-θ coordinates define the etching profile. The array ofdata points can be defined as an n×3 array, where n represents thenumber of points sampled and 3 represents the etch rate and two spatialdimensions. Of course, the choice of coordinates depends upon theparticular application.

Optionally, in a non-isothermal condition, an average etch rate ismeasured. By approximate integration of a time dependent etch rate,suitable starting point approximations for an etching rate constantpre-exponential and activation energy can be selected. The etch rate isintegrated over time (and temperature) using measured temperature-timedata (or history). An etched depth profile and the etching rate from theintegration can then be compared with actual data. A rate constant isappropriately readjusted and the aforementioned method is repeated asnecessary.

An etch rate constant (or a reaction rate constant) over diffusivity(k_(vo) /D) and an etch rate at an edge is calculated at step 105. Theetch rate constant over diffusivity correlates with data pointsrepresenting the etch rate profile. In x-y coordinates, the relationshipbetween k_(vo) /D and the relative etch rate u(x,y) is often defined asfollows:

where

a and b define substrate lengths in, respectively, an x-direction and ay-direction. ##EQU3##

In cylindrical coordinates, the relationship between the etch rateconstant over diffusivity k_(vo) /D and the relative etch rate u(r) isdefined as follows: ##EQU4## where a is an outer radius (or edge) of thesubstrate and I_(o) is a modified Bessel function of the first kind.

In step 106, a diffusivity is calculated for the particular etchants.The binary diffusivity D_(AB) may be calculated based upon the wellknown Chapman-Enskog kinetic theory equation: ##EQU5## where T is atemperature;

c is a total molar concentration;

M_(A) and M_(B) are molecular weights;

D_(AB) is a binary diffusivity;

σ_(AB) is a collision diameter; and

Ω_(D),AB is a collision integral.

The Chapman-Enskog kinetic theory equation is described in detail inpart III of R. B. Bird, W. E. Stewart, and E. N. Lightfoot, "TransportPhenomena," Wiley (1960) which is hereby incorporated by reference forall purposes. Of course, other techniques for calculating a diffusivitymay also be used.

The equivalent volumetric reaction rate constant k_(vo) is derived fromthe diffusivity as follows. ##EQU6## Once the reaction rate constantk_(vo) is extracted, the surface reaction rate constant k_(s) may beisolated from the previous equation as follows.

    k.sub.s =(k.sub.vo)d.sub.gap

Repeat steps 101-106 at different temperatures T₂, T₃ . . . T_(n) tocalculate additional reaction rate constants k(T₂), k(T₃) . . .k(T_(n)). The steps are repeated at least two times and more, andpreferably at least three times and more. Each temperature is at least5° C. greater than the previous temperature. Of course, the selection oftemperatures and trial numbers depend upon the particular application.

Extract an activation energy E_(act) for a first order reaction from thedata k(T₂), k(T₃) . . . k(T_(n)) at T₂, T₃ . . . T_(n) collected viastep 109 by way of the following equation. ##EQU7## The activationenergy is preferably calculated by a least square fit of data collectedat step 109 or any other suitable statistical technique. By way of thesame equation, the present method calculates surface reaction rateconstant k_(s) at any temperature.

In step 111, a concentration n_(o) at the substrate edge is calculated.The concentration n_(o) deduces from the following relationship:

    n.sub.o =R.sub.os /K.sub.s

where

R_(os) is an etch rate at the substrate edge.

From the concentration and the surface reaction rate, the particularetching step can be improved by way of adjusting selected etchingparameters.

In an alternative specific embodiment, a method to "tune" a plasmasource using a loading effect relationship (or equation) is illustratedby the simplified flow diagram 200 of FIG. 4. The method includes a step201 of measuring an etch rate against an effective etchable area A_(w).The effective etchable area changes by varying the number m of wafers inthe reactor, varying the size of the wafer, or the like. The effectivearea can be changed 209 by altering a gap between a wafer and its abovesurface 211, changing wafer quantity in the reactor 213, and varyingsubstrate support member dimensions 215. The method preferably occurs atconstant temperature and pressure. However, the effective etchable areamay also be varied by way of changing a temperature and/or a pressure.

The method calculates a uniformity value (step 217) from the measuredvalues of etch rate vs. effective area in steps 211, 213, and 215. Theuniformity is calculated by, for example:

    uniformity=100 ##EQU8## where R.sub.MAX is a maximum etch rate;

R_(MIN) is a minimum etch rate;

m is a sample number;

R_(i) is a general etch rate for an ith sample;

uniformity is a planarity measurement in percentage.

In a specific embodiment, a uniformity of about 90% and greater orpreferably 95% and greater indicates that the effective area of thesubstrate is substantially equal to the actual substrate area (step 221)via branch 216. Of course, other methods of calculating a uniformityfrom etch rates and effective areas may also be used depending upon theparticular application. Alternatively, an etching profile is measuredand the effective area A_(eff) is calculated (step 219) by way of, e.g.,the loading effect relationship.

At least two and more different effective etchable areas (step 223) aremeasured, or preferably at least three and more different etchable areasare measured. Alternatively, the flow diagram returns via branch 224 tostep 209, and takes another etch rate measurement at a differenteffective area. The flow diagram then turns to step 203.

In step 203, a supply of etchant S^(T) in the reactor is calculated.Based upon the different etchable areas a slope mA_(eff) deduces fromthe loading effect relationship as follows. ##EQU9## where R_(os) (m) isthe etching rate at the boundary between the plate stack zone andtransport zone when m substrates are present in the reactor. The firstterm includes a recombination term proportional to the total effectivearea A_(r) which acts to catalyze loss of etchant on reactor surfaces inthe reactor plus a convection term F. The second term is the loadingeffect relation, where the reciprocal etch rate is proportional to theamount of effective etchable substrate area A_(eff) times the number ofsubstrates m. When the etching across a substrate is uniform, A_(eff) isthe geometrical substrate area A_(w). When etching is nonuniform, on theother hand, A_(eff) is a function of k_(vo) /D and geometrical reactordimensions. The supply of etchant S^(T) may be calculated for adifferent plasma source or plasma source parameters such as temperature,pressure, or the like by repetition 207 of steps 201 and 203. By way ofthe supply of etchant to the reactor, other plasma source parameters maybe varied to obtain desired etching rates and uniformity for theparticular reactor.

Step 205 provides for the modification of chamber materials and the liketo reduce slope numerator (k_(r), A_(r) +F) in selecting the desiredetching conditions. The chamber materials can be modified to reduce, forexample, the recombination rate in the reactor. The recombination rateis directly related to the effective reactor recombination area A_(r).In step 205, the recombination rate can be adjusted by changing A_(r)via changing chamber material, coating chamber surfaces with, forexample, a product sold under the trademark TEFLON™ or KAIREZ™ and thelike, among others. Alternatively, the slope numerator flow term F isreduced when F contributes as a substantial loss term. Of course, theparticular materials used depend upon the application.

In step 207, the method changes plasma source parameters such as rfpower, flow rate, and the like to select desired etching conditions.Once one of the aforementioned parameters is adjusted, the methodreturns to step 201 via branch 208. At step 201, an etch rate vs.effective etchable area is measured and the method continues through thesteps until desired etching condition are achieved. Of course, othersequences of the aforementioned steps for tuning the plasma source mayalso exist depending upon the particular application.

FIG. 5 is a simplified flow diagram for a method of selecting a desireduniformity and desired etching parameters within selected ranges toprovide a desired etch rate for a particular etching process. Theetching parameters include process variables such as reactor dimensions,a pressure, a temperature, and the like for a particular substrate andreactants. Other etching parameters may also be used depending upon theparticular application.

In step 301, select a uniformity for the selected substrate and thereactants. The selected uniformity becomes an upper operating limit forthe reaction according to the present method. The upper operating limitensures a "worst case" uniformity value for an etched substrateaccording this method. Uniformity can be defined by, for example:

    uniformity=100 ##EQU10## where R.sub.MAX is a maximum etch rate;

R_(MIN) is a minimum etch rate;

m is a sample number;

R_(i) is a general etch rate for an ith sample;

uniformity is a planarity measurement in percentage.

In certain embodiments, the selected uniformity ranges from about 90%and greater or more preferably 95% and greater. Of course, otheruniformity values may be selected based upon the particular application.

Based upon the selected uniformity, use the selected uniformity as astating point to extract a plurality of reaction rate constants k_(s).The reaction rate constants may also be obtained by an input activationenergy for the etching process, among other techniques (step 303).Alternatively, calculate k_(s) at one or more temperatures, andpreferably two or more temperatures (step 303) from a plurality ofuniformity values. The uniformity values can be within the selecteduniformity or outside the selected uniformity.

In step 307, prepare an array of etching parameters including atemperature T, a pressure P, a characteristic reactor dimension, and auniformity value. In an embodiment, the characteristic reactor dimensioncan be a gap d_(gap) between the substrate and its adjacent surface. Thearray of etching parameters can be illustrated by way of a threedimensional plot.

An example of such array is illustrated by way of a three dimensionalplot 500 in FIG. 5A. It should be noted that the illustration is merelyan example of one application of the specific embodiment, and otherexamples can readily be determined by one of ordinary skill in the art.The plot includes a temperature axis, a pressure axis, and a gap axis.Each square region 501 represents a point defined by a specifictemperature, pressure, and gap. Each square region 501 also includes agray scale. Each different gray scale corresponds to a differentuniformity value. In this example, the darker gray scale values 505represent lower uniformity values than the lighter gray scale values507.

Based upon the array, compute locus of highest T, versus P and d_(gap),and of highest P, versus T and d_(gap) 511 where uniformity meets thespecification, e.g., the selected uniformity from step 301. All pointsbounded within the highest T, versus P and d_(gap), and the highest P,versus T and d_(gap) fall within the uniformity specification. Pointsoutside the highest T, versus P and d_(gap) and the highest P, versus Tand d_(gap) fall outside the uniformity specification. The points thatfall within the uniformity specification defines the calculateduniformity limit manifold having outer boundaries at P_(o) and T_(o).

In the calculated uniformity limit manifold, select a gap d_(gap), andadjust a locus of P and T below the calculated uniformity limit manifoldby a predetermined amount to allow for statistical and experimentalerror and process drift. This step defines a new uniformity limitmanifold, and ensures that points defined by a temperature, a pressure,and a gap, selected during subsequent steps fall within the selecteduniformity (step 301) despite any error or process drift from thecalculation. The new uniformity limit manifold includes outer boundariesat P_(i) and T_(i) which are respectively less than P_(o) and T_(o).

In step 311, a maximum edge etch rate R_(os) and supply of etchant froma plasma source (S) for a selected rf power, a reactant flow, apressure, a temperature, and a gap within the new uniformity limitmanifold is determined. The maximum edge etch rate can be used indefining a desired flow rate of source chemicals. Once the desired flowrate is determined, it should be held constant during subsequent stepsin the embodiment.

A step (step 313) of locating an intersection space of P<P_(i), T<T_(i),and a maximum etch rate (or an etchant supply) at selected rf powervalues is included. The intersection of space defines a maximum etchrate for the selected pressure P, temperature T, and gap d. Of course,other etching parameters may be adjusted depending upon the particularapplication.

The method provides a resulting etch rate from the etching reactionusing the aforementioned parameters which is compared with a desiredetch rate. If the resulting etch rate is too low (or high), change powerand/or reduce the effective etchable area, e.g., increase d_(gap),decrease number of substrates, use smaller substrates, and the like. Ofcourse, other sequences of steps may be used in selecting a desiredtemperature, pressure, gap, and other parameters to provide the desiredetch rate. The embodiment provides for a desired etch rate with aselected uniformity based upon a range of temperatures, pressures, andgap values, all within the selected uniformity specification.

Theoretical Model of Apparatus

1. Plasma Generating Zone

In the specific embodiment, the plasma generating zone can be modeled asa "black box" where etchant flow of reactant species from the plasmagenerating source is determined from an etching rate at the plate stackzone. In particular, the etching rate is proportional to a product n_(o)k_(s) of etchant concentration n_(o) above an etchable material filmsurface and an etching reaction rate constant k.sub. s. The etchingreaction rate constant k_(s) can be independently determined fromuniformity data previously noted. Since the relative change in n_(o)k_(s) and the absolute value of k_(r) (the effective surfacerecombination rate per unit reactor area) can be determined, n_(o) iseasily extracted and used to study the effects of discharge and surfaceparameters on production of etchant species in the plasma generatingzone. Accordingly, the efficiency of radical production by the plasmagenerating zone (the source term in a mass the mass balance of n_(o)) asa function of various parameters (pressure, power, temperature, etc.)can be extracted from indirect measurements.

2. Transport Zone

In the specific embodiment, etchant species concentrations in thetransport space zone are approximated as "well-mixed". In the well-mixedembodiment, substantially all etchant species in the transport spacezone are supplied by the plasma generating zone and are removed by atleast:

1) etching reactions in the plate stack zone; 2) recombination; or 3)convection by flow out of the reactor. A supply S^(T) of etchant fromthe plasma generating zone is equated to the three aforementioned lossterms as follows:

    S.sup.T =k.sub.r A.sub.r n.sub.o +mA.sub.eff k.sub.s n.sub.o +Fn.sub.o

where k_(r) A_(r) is an effective loss term with regard to recombinationeffects, k_(s) is an etching reaction rate constant, A_(eff) is aneffective etchable area of a substrate, n_(o) is the etchantconcentration, m is the number of substrates and F is the gas flow rateout of the reactor. The equation may be rewritten in the form of acanonical loading effect relationship: ##EQU11## where R_(o) (m) is theetching rate at the boundary between the plate stack zone and transportzone when m substrates are present in the reactor, and the first termincludes a recombination term proportional to the total effective areaA_(r) which acts to catalyze loss of etchant on reactor surfaces plusconvection F. The second term is the loading relation, wherein thereciprocal etch rate is proportional to the amount of effective etchablesubstrate area A_(eff) times the number of substrates m. When theetching across a substrate is uniform, A_(eff) is the geometricalsubstrate area A_(w). When etching is nonuniform, on the other hand,A_(eff) is a function of k_(vo) /D and geometrical reactor dimensions.Accordingly, A_(eff) becomes a function of parameters such astemperature, pressure, reactor configuration, and the like.

FIG. 6 shows etch rate data vs. the number of substrates in a reactoralong with a line corresponding to the loading effect relationship inthe form ##EQU12## where C_(o) =0.00030171936426 min/Å

and C₁ A_(w) =2.3003912550×10⁻⁵ are best fit constants for theconditions in FIG. 6. The equation gives an etching rate at the edge ofthe plate stack zone as a function of the number of substrates m andetchable exposed effective surface of a substrate A_(eff). Othervariables such as the temperature, etchant generation rate, flow rate,and reactor size parameters were held constant. While R_(os) (m) aswritten strictly applies to the etch rate at the edge of a substrate,when etching uniformity is high the etching rates at any other fixedrelative position on the substrates are related to R_(os) (m) by aconstant factor of proportionality, and so they will also conform to theform of these relations.

In the general case where etching is nonuniform across a substrate, theequivalent area A_(w) is smaller than the geometrical substrate area bya constant factor as a function of k_(vo) /D. It turns out that k_(s)can be independently deduced from the profile of the etching rate in thestack zone, and in turn permits the absolute value of n_(o) to becomputed from the etching rate R_(os) (m) at the edge of a substrate. Ifthe slope of the isothermal loading effect curve ##EQU13## is measuredalong with etching uniformity, the rate of etchant supplied by thesource S^(T) can be found by for substituting A_(eff) (k_(vo) /D)evaluated on the basis of etching uniformity measurements.

3. Stack Zone

For etchant mass transport from the transport zone into the plate stackzone, the distance between stacked wafers d_(gap) is small compared tothe lineal dimensions of a substrate in the embodiment. Consequently, itwill be assumed that the concentration is substantially uniform in theaxial z direction and there is equi-molal, isothermal, and isobariccounter-diffusion (e.g., no net flux, Σn₁ =0) in the x and y directions.Since the ashing reaction is proportional to n_(o), and O-atomconsumption is proportional to the ashing rate, the continuity equationfor O-atoms in two dimensions becomes: ##EQU14## where k_(vo) is thevolume equivalent surface reaction rate constant, and v is the diffusivevelocity of oxygen atoms. Inserting Fick's law

    n.sub.o v =-D∇n.sub.o

the diffusion equation is obtained ##EQU15## And at steady-state in twodimensions and where D is not a function of spatial coordinate(s), it isrewritten as ##EQU16## where u(x,y)=n_(o) (x,y)/n_(o0) and n_(o0) is theetchant concentration at the outer edges of the substrates. The boundaryconditions are therefore u=1. The equation is cast in dimensionless formas ##EQU17## where L_(x) and L_(y) are characteristic independentlengths and widths of substrates. From this equation, it is clear thatu(x/L_(x), y/L_(y)) is a function solely of k_(vo) /D and the boundaryconditions. Consequently, if experimental values of u(x/L_(x), y/L_(y))are measured at two positions on the substrate (i.e., at the center andedge), two algebraic equations based on this measurement can be used toeliminate n_(o) /n_(o0) and solve for k_(vc) /D. The diffusivity D canbe calculated to good accuracy with the Hirshfelder equation; hence,k_(vo) is measured with this procedure.

For circular substrates, there is only one independent dimension (e.g.,where r=a is the substrate radius). At steady state in one dimensionalcylindrical coordinates the equation can be written: ##EQU18## whereu(r)=n_(o) (r)/n_(o0) and the boundary condition is u(a)=1 at thesubstrate (wafer) edge.

In the subsequent sections, analytic solutions to these relationshipsare developed for rectangular and circular substrates (e.g., for flatpanel display substrates and semiconductor wafers). The framework isused to derive uniformity relationships for flat panel resist strippingequipment.

EXAMPLES

1. Circular Substrate (Wafer) Stacked Etcher

To prove the principles of the aforementioned embodiments, the presentmethod and apparatus was applied to etching of circular substrates in astacked etcher. Of course, the present method and apparatus can beapplied to other geometries and etcher types. The present example istherefore not intended to be limiting in any way. The present method andapparatus is applied to the circular substrates as illustrated by way ofFIG. 7. The present method relies upon etching of substrate material Sby way of oxygen using a reaction which is substantially chemicaletching.

An illustration of a circular substrate according to the presentinvention is shown in FIG. 8. Assume that the distance d_(gap) betweenstacked wafers is relatively small compared to the wafer radius a suchthat d_(gap) <<a. Based upon the assumption, the oxygen concentrationwill be substantially uniform in the axial direction z. Accordingly,only radial diffusion in the r-direction needs consideration. Assumingan equi-molal counterdiffusion ##EQU19## and an isobaric and isothermalstack zone, the problem reduces to two dimensions and becomes ##EQU20##where u(r)=n_(o) (r)/n_(o0). The boundary condition is u(a)=1 at a waferedge, and the solution of the equation becomes ##EQU21## where I₀ and K₀are modified Bessel functions of the first and second kind,respectively, and c₁ and c₂ are constants. For a finite, normalizedoxygen concentration u(0) at the center of the wafer, the equationrequires c₂ =0. The remaining boundary condition of u(a)=1, sets thesolution: ##EQU22## Note that the functional form u(r) describes boththe relative etch rate profile R_(o) (r)/R_(o) (a) and the relativeoxygen atom etchant concentration n_(o) (r)/n_(o) (a). The relative etchrate profile can easily be obtained by measuring an etching rate profileon a circular substrate made by way of the present method.

FIG. 9 is a simplified plot of a normalized stripping rate vs. radialdistance from a wafer center for the circular substrate example. Theplot shows a profile of u(r) for k_(vo) /D=0.1, and an a=150 mm. As canbe seen, the normalized stripping rate is lower at a center region ofthe wafer, and increases to 1 at the wafer edge. Based upon a slope ofthe plot, a reaction rate coefficient can be extracted by way of adiffusivity.

2. Rectangular Substrate Stack Asher

To further provide the principle and operation of the present-method andapparatus, the present method and apparatus is applied to a rectangularsubstrate configuration in a stack asher. Again, the present exampleshould not be taken as limiting the scope of the claims describedherein, but is merely an example. An analytical solution for etchingprofiles in the stack zone are derived for etching/ashing a stack ofrectangular substrates as illustrated in FIG. 10. The rectangularsubstrate can be a flat panel display such as a liquid crystal display(LCD) plate and the like in the coordinate system of FIG. 10. To solvean equation for the present rectangular configuration where D is notdependent upon spatial coordinates, write the solution as:

    u=u.sub.1 +u.sub.2

where u₁ is satisfied by the following equation ##EQU23## where u₁ =0 aty=±b/2; and u₂ is a solution that is 0 at x=±a/2.

The solution for u₁ (x,y)=X(x)Y(y) is obtained by a separation ofvariables as follows. ##EQU24## The sign of the sum decomposing λ² ischosen so that X(x) and Y(y) both have real values, as shown below.Since the boundary conditions on Y(y) are:

    Y(-b/2)=Y(b/2)=0

the solution is,

    Y=c.sub.y cos λ.sub.y y.

From the boundary conditions, c_(y) =m/b where m=1,3,5, . . . Similarly,the solution for X is ##EQU25## The general solution is the sum:##EQU26## where c_(m) =0 for m=0,2,4, . . . to satisfy the boundaryconditions. Setting u₁ (a/2,y)=f(y), where f(y) is the even-functionsquare wave of magnitude 1, the Fourier series is obtained, ##EQU27##and after the integration ##EQU28## which is zero when m is even, asrequired. Thus, the u₁ part of the solution can be written ##EQU29##Note that u₁ (a/2,y)=1 for (-b/2<y<b/2). The solution for u₂ can beobtained in a similar way. The solution is then ##EQU30## where m isodd. As b→∞, this approaches the solution for 1 -dimensional diffusion(corresponding to an infinitely long strip): ##EQU31##

The previous two-dimensional equation is now applied to interpret ashinguniformity data and predict uniformity and the atomic oxygenconcentration profile n_(o) along the surface of a substrate forselected operating conditions. To use the relationship, values of k_(vo)and D are required. For atomic oxygen diffusing through O₂, diffusivitywas computed as D(cm² /s)=0.044T^(3/2) (T is in K) using relations in J.O. Hirschfelder, C. F. Curtiss, R. B. Byrd, "Molecular Theory of Gasesand Liquids," pp. 538-541 and 578-582, John Wiley & Sons, 2nd Printing(1963), which is hereby incorporated by reference for all purposes. Ofcourse, other techniques for calculating the diffusivity also exist.

In general, k_(vo) will be a function of at least gap, resistcomposition, temperature, and other parameters. In an example, k_(vo) isunknown, although the activation energy for resist ashing isconventionally reported to be in the 11-12 kCal range from industryliterature. However, the solutions for u(x,y) depend only on k_(vo) /Dand geometrical chamber dimensions such as gap (as incorporated intok_(vo)), a, b, and the like. Accordingly, k_(vo) /D is deduced from theetching rate profile, as previously described.

In particular, k_(vo) /D can be obtained from measurements of the amountof resist removed at two independent points (points where thetheoretically predicted etch depth ratios u(x₁,y₁), u(x₂,y₂) are unequalby solving the appropriate equation for k_(vo) /D and substituting forD(T,P). But the present example used a more robust procedure: determinek_(vo) /D from a least squares fit to the entire experimental etchprofile data set taken by a conventional stylus profilometer.

FIG. 12 shows an experimental etching profile data taken on a 30×30 cmresist-covered substrate spin-coated with 2.1 microns of MCPR 200 resist(Mitsubishi Chemical Corp., equivalent to Tokyo Ohka Kogyo Co. OFPR800). A vertical axis 1201 defines an ashing rate R_(os) with respect toan x-direction 1203 and a y-direction 1205. A grid pattern 1207represents a "fitted" surface region via aforementioned equationrepresenting ashing rates. Actual data points for each ashing rate aredefined as the circular points 1211, and plots representing the fittedsurface region are defined as cross points 1209. Ashing rate is greateraround the periphery of the substrate, than substrate center regions.

The reactor held 1.1 mm thick substrates with a 28.9 mm gap (d_(gap))above the wafer. A 4 kW rf power source sustained a plasma with pureoxygen gas flowing into the reactor at 3 liters/min. Thermocouplesensors and heaters kept the reactor chamber and substrates at T=220° C.during the etch process, and a throttle valve maintained pressure atP=1.2 Torr. Etching occurred for 5 min. Resist thickness was measuredbefore and after etching using a Nanometrics Model 210 Nanospec AutoFilm Thickness Monitor. The surface of FIG. 12 represents a leastsquares fit to the aforementioned equation for u(x,y) with k_(vo) /D asthe only adjustable parameter. The least squares fit gives k_(vo)/D=0.047. At P=1.27 Torr and T=493 K into D(cm² /s)=0.044T^(3/2) yieldsD=400 cm² /S. By way of the relationship k_(vo) /D=0.047, the etch rateconstant is now k_(vo) =19.5 sec.⁻¹. In the manner, e.g., by fittingprofile data to the solution for given substrate geometry, k_(vo) can bemeasured under various process conditions. By way of k_(vo), otherparameters such as n_(o), k_(s), and the like may also be calculated.

Once k_(vo) is known as a function of temperature, ashing rate anduniformity can be calculated as a function of reactor size parameters(a,b) and process variables (p, T, and n_(o)). While the etching rate isproportional to n_(o0), n_(o0) does not affect the etch depth profileand need not be known to compute k_(vo). However, after k_(vo) isobtained, n_(o0) can be computed from the experimentally measuredetching rate per R_(os) =k_(s) n_(o0). The procedure applies up toendpoint (endpoint is the time at which resist has been "stripped" andis no longer covering the region of the substrate where etching wasfastest). At endpoint, resist begins to be cleared from the substrate sothat etchable area changes. Hence, n_(o0) will start to change(increase) after endpoint. The magnitude of n_(o0) during thesteady-state period when resist is etching controlled by the plasmasource, the number of substrates loaded into the reactor and (possibly)convective loss.

Predicting Etch Rate

The effect of profile uniformity on loading can be explicitly accountedfor by defining a profile-average substrate area A_(eff) ##EQU32## sothat n_(o0) k_(vo) A_(eff) is the per substrate etchant consumption withnonuniformity resulting from effects of diffusion and reaction takeninto account. Then for given plasma source (etchant supply), the etchrate/loading effect equation becomes: ##EQU33## All of the terms can becomputed explicitly from etch rate profile data, except for the rate ofetchant production by the source. The etchant production rate can becomputed from two measurements of etching rate when changing k_(vo)A_(eff). A_(eff) can be changed either by changing the number ofsubstrates or changing the etch rate profile (with constant etchantsupply).

The present invention provides a method of selecting uniformity inchemical plasma etching as a function of processing parameters. Thepresent invention also provides for a method of measuring absolutegas-surface reaction rates in commercial processing equipment withoutthe benefit of sophisticated diagnostic equipment.

Gas-surface radical reaction rates are often needed for the design ofplasma processing equipment and for selection of desired reactionconditions. Unfortunately, few data are available on absolute reactionrates in systems of practical interest in the prior art. Mostexperimental data have been taken in difficult flow tube experiments, orby related techniques which require reactant concentrations to bequantified using sophisticated methods such as gas-phase titration,laser fluorescence or mass spectrometry. These measurements requiregreat care and specialized instrumentation. In contrast, the presentinvention describes a technique for measuring etching rate constants. Itcan be carried out in commercial processing equipment and the like, andit does not require sophisticated instrumentation, direct radicalmeasurements, or the like. An isothermal reaction rate constant may bederived from a single measurement of etching uniformity. From thisinformation, the etching rate uniformity as a function of substratespacing and pressure can be computed. If experimental data on uniformityare taken at several temperatures, an intrinsic activation energy can bederived and the effects of temperature can be expressed analytically.

While the above is a full description of the specific embodiments,various modifications, alternative constructions and equivalents may beused. For example, while the description above is in terms of a plasmaetching method, it would be possible to implement the present inventionwith other etching methods or the like.

Therefore, the above description and illustrations should not be takenas limiting the scope of the present invention which is defined by theappended claims.

What is claimed is:
 1. A method of determining a surface reaction rateconstant comprising:providing apparatus comprising a substrate therein,said substrate comprising a top surface and a film overlying said topsurface, said film comprising a top film surface; processing said topfilm surface to define a non-uniform etching profile on said film, anddefining etch rate data comprising an etch rate and a spatial coordinatewhich defines a position within said non-uniform etching profile on saidfilm on said substrate, said processing comprising a reaction between agas phase etchant and said film; and extracting said surface reactionrate constant from said etch rate data.
 2. The method of claim 1 whereinsaid processing is diffusion limited.
 3. The method of claim 1 whereinsaid spatial coordinate includes a radius and an angle.
 4. The method ofclaim 1 wherein said spatial coordinate includes an x-direction and ay-direction.
 5. The method of claim 1 wherein said extracting correlatessaid surface reaction rate constant over a diffusivity with said etchrate, said etch rate being defined by said non-uniform etching profile.6. The method of claim 1 wherein said etch rate is defined by saidnon-uniform etching profile at selected spatial coordinates over a time.7. The method of claim 1 wherein said processing is an ashing method. 8.The method of claim 7 wherein said ashing method comprises reactantsincluding an oxygen and a photoresist.
 9. A method of designing areactor comprising the steps of:providing an apparatus comprising asubstrate therein, said substrate comprising a top surface and a filmoverlying said top surface, said film comprising a top film surface;processing said top film surface to define a non-uniform etching profileon said film, and defining etch rate data comprising an etch rate and aspatial coordinate which defines a position within said non-uniformetching profile on said film of said substrate, said processingcomprising a reaction between a gas phase etchant and said film; andextracting a surface reaction rate constant from said etch rate data.10. The method of claim 9 wherein said processing at a position on saidnon-uniform etching profile is diffusion limited.
 11. The method ofclaim 9 wherein said spatial coordinate which defines said positionalong said non-uniform etching profile includes a radius and an angle.12. The method of claim 9 wherein said spatial coordinate which definessaid position within said non-uniform etching profile includes anx-direction and a y-direction.
 13. The method of claim 9 wherein saidextracting correlates said surface reaction rate constant over adiffusivity with said etch rate, said etch rate being defined by saidnon-uniform etching profile.
 14. The method of claim 9 wherein said etchrate is defined by said non-uniform etching profile at selected spatialcoordinates over a time.
 15. The method of claim 9 wherein saidprocessing is an ashing method.
 16. The method of claim 15 wherein saidashing method comprises reactants including an oxygen and a photoresist.17. The method of claim 9 wherein said surface reaction rate constant isused to design a plasma etching apparatus.
 18. The method of claim 17wherein said plasma etching apparatus is a co-axial reactor.
 19. Themethod of claim 17 wherein said surface rate reaction constant is usedto design a second plasma etching apparatus.
 20. A fabrication method,using a plasma etching apparatus, said method comprising:providing asubstrate selected from a group consisting of a semiconductor wafer, aplate, and a flat panel display, said substrate comprising a topsurface; forming a film overlying said top surface, said film comprisinga top film surface; processing said top film surface to define anon-uniform profile on said film, and defining etch rate data comprisingan etch rate and a spatial coordinate which defines a position withinsaid non-uniform etching profile of said film on said substrate, saidprocessing comprising a reaction between a gas phase etchant and saidfilm; and extracting a surface reaction rate constant from said etchrate data.